Dynamic and game theoretic modelling of societal growth, structure and collapse

Abstract

The dynamics and structure of societies have long been a puzzle to archaeologists, historians and social scientists in general. In particular, increases in social inequality and the possibility of societal collapse are two deeply distressing prospects for any society. In this three paper thesis we provide two contributions to the literature of societal collapse and one regarding the emergence of social inequality.
In the first article we present a mathematical model of Easter Island and show that the collapse can be modelled as a supercritical Hopf bifurcation where the critical parameter is the harvesting rate of resources. This suggests an universal mechanism by which societal collapse can be understood quantitatively. In addition, we show that societies coupled together can be more robust against collapse, which means that, within a larger region of parameter space, a sustainable outcome can occur for both societies than in the case when the societies are isolated. In particular, if at least one society has a harvesting rate below the critical value, then collapse can be prevented for the entire system.
In the second article we build a dynamical system model of the Maya civilisation taking into account the main specialisations of the population: swidden and intensive agriculturalists, and monument builders. The archaeological record for population growth and monument construction is accurately reproduced, with the model calibration close to archaeologically determined values for the parameters. We show that if, after the year 550 CE, a significant part of each new generation moved from swidden to using intensive
agricultural methods, then this would explain the rapid population growth and the subsequent collapse. This conclusion is reached irrespective of the impact of drought. Furthermore, the model is shown to also undergo a supercritical Hopf bifurcation when the harvesting rate is high. An extensive sensitivity analysis indicates that the model predictions are robust under parameter changes, which means that the period around the year 550 CE played a key role in the collapse.
In the third article we address the issue of social inequality by considering games on networks. In contrast to large parts of the literature, we investigate for what network structure a system of linked agents can exhibit maximally rational strategic behaviour. The agent’s strategies are quantified through the quantal response equilibrium, and the network is optimised so that the strategies are as close as possible to the Nash equilibrium. Previous work has argued that a scale-free topology maximises system rationality.
In contrast, we show that a core-periphery structure emerges, where a small set of nodes enjoy higher degrees than the majority, which are leaf nodes. In symmetric games the difference in degrees between the two node types are stark, whereas in asymmetric games the difference is less notable.
Taken together, the different parts of this thesis highlight and explain dynamical and large-scale structural features in societies as seen throughout the history of the world. Thus, this work can help deepen our understanding of complex social phenomena.

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